Foundations of Physics

, Volume 20, Issue 11, pp 1365–1378 | Cite as

Random quantum states

  • William K. Wootters
Part II. Invited Papers Dedicated To John Stewart Bell


This paper examines the statistical properties of random quantum states, for four different kinds of random state:(1) a pure state chosen at random with respect to the uniform measure on the unit sphere in a finite-dimensional Hilbert space;(2) a random pure state in a real space;(3) a pure state chosen at random except that a certain expectation value is fixed;(4) a random mixed state with fixed eigenvalues. For the first two of these, we give examples of simple states of a model system, the kicked top, which have the statistical properties of random states. Interestingly, examples of both kinds of randomness can be found in the same system. In studying the last two kinds of random state, we obtain new results concerning the application of information theory to quantum systems.


Hilbert Space Information Theory Quantum State Quantum System Unit Sphere 
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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • William K. Wootters
    • 1
    • 2
    • 3
  1. 1.Santa Fe InstituteSanta Fe
  2. 2.U.S.A. Center for Nonlinear Studies and Theoretical DivisionLos Alamos National LaboratoryLos Alamos
  3. 3.U.S.A. Department of PhysicsWilliams CollegeWilliamstownUSA

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